FRG:Collaborative Research: Chemically-active Viscoelastic Mixture Models in Physiology: Formulation, Analysis, and Computation

该项目涉及几个复杂生物过程的数学模型的开发和分析，每个过程对基础和健康科学都具有重要意义：细胞起泡及其通过细胞外基质在细胞运动中的作用，动脉血液凝固中的血小板沉积和纤维蛋白凝胶化，粘蛋白分泌及其在胃中酸运输中的作用，高尔基体的蛋白质分类和运输。尽管这些过程的生物学细节有很大不同，但一个共同的主题是，每个过程都涉及复杂的粘弹性材料混合物，其行为是由力学、流动、物理结构和化学的动态相互作用决定的。这些过程的数学描述需要描述多相流的方程，成分、结构和化学的演变，以及应力与成分/结构之间的关系。结合这些元素的复杂模型的解决和分析将带来大量的数学和计算挑战。为了应对这些挑战，研究人员将开发和应用先进的数值算法，以获得对这些重要生理过程的功能机制的基本见解。这项工作将在理解复杂材料的力学和动力学在生物系统功能中的重要作用方面取得新的重要进展。反过来，这将有助于改善包括冠状动脉疾病、癌症和代谢性疾病在内的一系列严重疾病的诊断和治疗。这项工作还将有助于更好地理解复杂材料，并有助于设计新颖的新材料，以应对紧迫的技术挑战。此外，新的计算算法的设计将导致在科学和工程中使用高性能计算的新能力。该项目的高度跨学科性质将为培训青年科学家以新的多学科方法研究科学提供许多机会。许多重要的生理过程涉及不同类型的物质（例如，水和细胞或水和聚合物凝胶）之间的相互作用，它们彼此相对移动。材料之间的物理相互作用可以受到化学反应的强烈影响，而化学反应反过来又受到材料运动和其他相互作用的影响。更好地了解这些复杂系统是如何工作和调控的，对于理解这些重要过程以及如何操纵它们以改善人类健康至关重要。因为这些过程受物理和化学原理和性质的支配，因为这些原理和性质可以用数学来表示，所以数学工具可以用来解决这些问题。通过数学分析和计算模拟，可以开发对材料行为的新见解，并可以获得丰富的数据，以补充从传统实验室实验中获得的数据。因此，在这个项目中，数学和实验研究者的结合有望在重要的生理和病理情况，包括血液凝固、代谢和癌症转移方面带来重要的新见解。此外，该项目开发的数学和计算工具将影响非生物复杂材料的发展，以应对紧迫的技术挑战。

This project concerns development and analysis of mathematical models of several complex biological processes, each with major importance to the fundamental and health sciences: cellular blebbing and its role in cellular locomotion through extracellular matrix, platelet deposition and fibrin gelation in arterial blood clotting, mucin secretion and its role in acid transport in the stomach, protein sorting and trafficking by the Golgi apparatus. Although the details of the biology of these processes are vastly different, a common theme is that each involves a complex viscoelastic material mixture whose behavior is determined by the dynamic interplay of mechanics, flow, physical structure, and chemistry. The mathematical description of these processes requires equations describing multiphase flow, the evolution of composition, structure and chemistry, and the relationship between stresses and composition/structure. The solution and analysis of sophisticated models that combine these elements will pose substantial mathematical and computational challenges. To meet these challenges, the investigators will develop and apply advanced numerical algorithms to gain fundamental insights into the mechanisms of function of these important physiological processes. This work will lead to novel and important advances in understanding the essential role of the mechanics and dynamics of complex materials in the function of biological systems. This, in turn, will support improved diagnosis and treatment of a range of serious medical disorders including coronary artery disease, cancer, and metabolic disease. The work will also lead to better understanding of complex materials in general and contribute to the design of novel new materials for meeting pressing technological challenges. Furthermore, the design of new computational algorithms will lead to new capabilities in the use of high-performance computing in science and engineering. The highly interdisciplinary nature of the project will provide many opportunities for training young scientists in the new multi-disciplinary approach to science.Many important physiological processes involve interactions between materials of different types (for example, water and cells or water and polymer gels) and which move relative to one another. The physical interactions between the materials can be strongly influenced by chemical reactions, and the chemical reactions in turn are influenced by the materials' motion and other interactions. Better insight into how such complex systems work and are regulated is critical to understanding these important processes and how they can be manipulated to improve human health. Because these processes are governed by physical and chemical principles and properties, and because these principles and properties can be expressed mathematically, mathematical tools can be brought to bear on these problems. Through mathematical analysis and computational simulations, new insights into the materials' behavior can be developed and a wealth of data can be obtained that complements the data obtainable from traditional laboratory experiments. Hence the combination of mathematical and experimental investigators brought together in this project is expected to lead to significant new insights in important physiological and pathological situations including blood clotting, metabolism, and cancer metastasis. Further the mathematics and computational tools developed in the project will impact the development of non-biological complex materials to meet pressing technological challenges.